X-ray Timing of the Enigmatic Neutron Star Rx J0720.4−3125

RX J0720.4−3125 is the third brightest neutron star in the soft X-ray sky and has been a source of mystery since its discovery, as its long 8-s period separates it from the population of typical radio pulsars. Three models were proposed for this source: a neutron star accreting from the interstellar medium, an off-beam radio pulsar, or an old, cooling magnetar. Using data from Chandra, ROSAT, and BeppoSAX we are able to place an upper limit to the period derivative, | ˙ P | < 3.6 × 10 −13 s s −1 (3-σ). While our upper limit on ˙ P allows for the accretion model, this model is increasingly untenable for another similar but better studied neutron star, RX J1856.5−3754, and we therefore consider the accretion model unlikely for RX J0720.4−3125. We constrain the initial magnetic field of RX J0720.4−3125 to be 10 14 G based on cooling models, suggesting that it is not and never was a magnetar, but is instead middle-aged neutron star. We propose that it is either a long-period high-magnetic field pulsar with ˙ P ∼ 10 −13 s s −1 similar to PSR J1814−1744, or a neutron star born with an initial period of ≈ 8.3 s and ˙ P ∼ 10 −15 s s −1. The proximity of RX J0720.4−3125 is strongly suggestive of a large population of such objects; if so, radio pulsar surveys must have missed many of these sources.